question_answer

From a number of apples, a man sells half the number of existing apples plus 1 to the first customer, \[\frac{1}{3}\,\,\text{rd}\]of the remaining apples plus 1 to the second customer and \[\frac{1}{5}\,\,\text{th}\]of the remaining apples plus 1 to the third customer. He then finds that he has 3 apples left. If number of apples the man sold to the first customer, second customer and third customer are P, Q and R respectively, then find the value of: \[\frac{{{(P+Q)}^{3}}+{{(P+R)}^{2}}}{(Q+R+2)}\]

A)  826                             

B)  579

C)  496                             

D)  443

E)  None of these